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Question
The mid-point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a + 1). Find the values of a and b.
Solution
Mid-point of (2a, 4) and (−2, 2b) is (1, 2a + 1),
Therefore using mid-point formula, we have:
`x = (x_1 + x_2)/2 `
`1 = (2a - 2)/2`
1 = a − 1
a = 2
` y = (y_1 + y_2)/2`
`2a + 1 = (4 + 2b)/2`
2a + 1 = 2 + b
2 × 2 + 1 – 2 = b
b = 5 – 2 = 3
Therefore, a = 2, b = 3.
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